How does one 'Describe fully a single translation'?

My object has been reflected twice, do I just say 'reflected on x=_ then on y=_'?

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- May 20th 2010, 12:21 PMMukilabTranslation
How does one 'Describe fully a single translation'?

My object has been reflected twice, do I just say 'reflected on x=_ then on y=_'? - May 20th 2010, 10:29 PMGrandadCombining two reflections
Hello MukilabAre you sure the question says 'a single

*translation*'? The combined transformation will be a translation only if the two mirror-lines are parallel. And from what you say about '$\displaystyle x =... $' and '$\displaystyle y =...$', it sounds as if they aren't.

Does the question say 'Describe fully a single*transformation*...'?

When one reflection is followed by a second reflection in mirror-lines that are not parallel, this is equivalent to a rotation, whose centre is at the point where the mirror-lines meet, through twice the angle between them.

It sounds as if your mirror-lines are at right-angles, so the rotation will be through a half-turn.

Does that help to answer your question?

Grandad - May 21st 2010, 08:27 AMMukilab
It can't just be a rotation, it doesn't make sense.

It is 'single transformation'

Here are the coordinates of the three triangles

A= 0,3 1,3 and 1,5

B= 3,0 3,1 and 5,1

C= 5,3 6,3 and 5,5

Describe the translation of A onto B. Is this a reflection around line y=x? - May 21st 2010, 12:37 PMGrandad
Hello MukilabAgain, you have used the word 'translation' when you meant 'transformation'.

I was guessing what the answer might be, based on the incomplete information you gave me in your first post. You are right: the transformation that maps A onto B is a reflection in the line $\displaystyle y = x$.

B is then mapped onto C by a rotation through $\displaystyle 90^o$ anticlockwise, centre $\displaystyle (3,3)$.

The single transformation that maps A onto C is a reflection in the line $\displaystyle x = 3$.

Grandad